It’s surprising what can creep into a stock index nowadays. A few months ago, responding to the increasing importance of China’s capital markets, MSCI decided to start including its domestically listed companies in major emerging-markets indices. The result is that many British pensioners, if they looked into it, are now quite likely to find that they have gone into business with the Chinese government.

China’s state-owned enterprises (SOEs) dominate its economy. A recent report by the Asia Society details to what degree: they account for 56pc of domestically-listed firms’ total revenues and 40pc of their total market capitalisation.

And as those figures indicate, they tend not to be investors’ favourite stocks. They achieve much lower valuations than China’s private companies and there is good reason for that. On average, they generate returns of 3.9pc a year, compared to 9.9pc for private firms.

Outside China, the role of its SOEs has become increasingly controversial. Whether they are undercutting steel prices, transferring technology from foreign investors or overbidding for assets abroad, their heavily subsidised activities are very near the top of the complaints list by European, Japanese and US trade negotiators.

In China itself, with debt levels shooting up and growth slowing, the government has repeatedly paid lip service to the idea that overhauling its sprawling state corporate empire will be a key next stage in its economic reforms.

A deeper look at their corporate governance arrangements, however, suggests otherwise.

On paper, the reforms have come a long way. The Asia Society’s report documents how they began alongside China’s great “opening up” in the Seventies and Eighties, when the government began to convert state “production units” into separate enterprises with more autonomy over their decisions. By the 1990s, the sector’s growing losses forced Beijing to take further action.

Over the next 15 years, the government introduced a more modern company law, established an authority and regulations for listed companies and mandated the creation of boards with external directors. On the back of these reforms, there was a rush to raise capital via share offerings and huge loans.

This looks like impressive progress. SOEs have shrunk in relative terms. In 2002, for example, they owned 60pc of all China’s industrial assets, versus 30pc today. The enormous growth in their debt levels, which went from being worth 70pc of China’s GDP in 2002 to 140pc in 2016, has moderated in the last year.

Unfortunately, however, tentative moves to boost the power of private shareholders over these corporate behemoths have gone into reverse under Premier Xi Jinping. The corporate governance reforms have never really achieved lift-off and investors, judging by the lower valuations they give SOEs, know it. At every stage, they have faced the power of entrenched control by managers, who often funnel cash up and out of the businesses.

In 2002, an investigation of 1,175 listed companies by Chinese authorities found that more than half had misused company funds to the tune of $14bn (£11bn). A concerted effort to combat SOE corruption by former premier Hu Jintao never quite cracked the problem. The lesson drawn from that by Xi, alas, seemed to be that that the right vehicle for solving the issue is the Chinese Communist Party.

His administration has therefore set about entrenching and furthering the party’s role in SOE governance. Every state company is currently expected to have a party committee that is separate from its board of directors.

In theory, there is a clear separation in roles. The board is in charge of commercial decisions and the party committee tackles corruption and communicates party policy and campaign messages. In practice, the party wields ultimate control. First and foremost, it is party officials (and regulators) who hire and fire senior management and, in practice, must approve the appointment even of independent directors.

Any ambitious young thing making her career in a state enterprise will know precisely where patronage comes from – and it isn’t the board.

Secondly, there is a usually a significant overlap between members of senior management and members of a company’s party committee, so even if the roles are theoretically separate, the people holding them aren’t.

Lastly, the Communist Party’s formal role in making decisions is growing. They are allowed to involve themselves in any “major” decisions, loosely defined, and as of 2016 are expected to start demonstrating “core leadership” of state-owned companies, expanding their presence further.

The upshot is that China’s enormous state sector is moving clearly back towards greater government and party control. Beijing is trying to rationalise the sector by encouraging mergers and has a stated aim of furthering “mixed ownership” – that is, getting more private cash into the system. But investors aren’t total mugs. They aren’t going to start handing increasingly large cheques to companies whose leadership answers to an entirely different set of interests.

Even if there are improvements in the regulations and governance of listed companies, it means little if those listed entities still answer to opaquely governed group boards appointed by state and party officials.

China’s growth might be slowing, but this trend is more worrying to its investors and trading partners. The world’s second-biggest economy is supposedly moving on to a new stage of development, in which consumption, market discipline and foreign investment will be allowed to play a greater role in allocating capital. For that to take hold in any meaningful way, however, Beijing needs to be prepared to give up more control over the state sector. So far, there is little sign that it is willing to do so.